Question

Triangles ABC and DEF are similar. Find the lengths of AB and EF.

Right triangles ABC and DEF. Side AB is 5x, side BC is 4, and hypotenuse AC is unknown. Side DE is 5, EF is x, and hypotenuse DF is blank.
a) AB = 2; EF = 10
b) AB = 10; EF = 2
c) AB = 20; EF = 4
d) AB = 4; EF = 20

Answer 1

To find the lengths of AB and EF, we can use the fact that triangles ABC and DEF are similar. In similar triangles, the corresponding sides are proportional. The lengths of AB and EF are both 5x.

Step-by-step explanation:

To find the lengths of AB and EF, we can use the fact that triangles ABC and DEF are similar. In similar triangles, the corresponding sides are proportional. Given that AB is 5x and BC is 4, we know that the ratio of AB to BC is 5x:4. We can set up an equation:

5x/4 = AB/BC

Cross-multiplying, we get:

4 * AB = 5x * BC

Simplifying:

AB = (5/4) * x * BC

Since BC is 4, we can substitute this value in:

AB = (5/4) * x * 4

AB = 5x

Similarly, for triangle DEF, we know that EF is x. So, we have EF = x.

Therefore, the lengths of AB and EF are both 5x.